{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MZJSVAHYM2DWULJ5KVUUTNIHHJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e6217bcff23cc56c2c3430063700926712c37d2a323787f4665ef3ae3859b462","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-12T20:00:05Z","title_canon_sha256":"e0d71630587a74e3b443560485ebeb8ab269b1d5899f96a5eaf7ea56e04c4d18"},"schema_version":"1.0","source":{"id":"1807.04804","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04804","created_at":"2026-07-05T00:50:00Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04804v3","created_at":"2026-07-05T00:50:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04804","created_at":"2026-07-05T00:50:00Z"},{"alias_kind":"pith_short_12","alias_value":"MZJSVAHYM2DW","created_at":"2026-07-05T00:50:00Z"},{"alias_kind":"pith_short_16","alias_value":"MZJSVAHYM2DWULJ5","created_at":"2026-07-05T00:50:00Z"},{"alias_kind":"pith_short_8","alias_value":"MZJSVAHY","created_at":"2026-07-05T00:50:00Z"}],"graph_snapshots":[{"event_id":"sha256:e53dfd3fa12e2287f4e489caaa8bdd662bb951e2c953f673f663442d5774cdc1","target":"graph","created_at":"2026-07-05T00:50:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1807.04804/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an FPTAS and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model on bounded-degree expander graphs. The results apply, for example, to random (bipartite) $\\Delta$-regular graphs, for which no efficient algorithms were known for these problems (with the exception of the Ising model) in the non-uniqueness regime of the infinite $\\Delta$-regular tree. We also find efficient counting and sampling algorithms for proper $q$-colorings of random $\\Delta$-regular bipartite graphs when","authors_text":"Matthew Jenssen, Peter Keevash, Will Perkins","cross_cats":["math.CO","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-12T20:00:05Z","title":"Algorithms for #BIS-hard problems on expander graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04804","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f0c5cf3af2d48df7a05b0f0037e267e6b695d159cbcdeb569efdf287ca087266","target":"record","created_at":"2026-07-05T00:50:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e6217bcff23cc56c2c3430063700926712c37d2a323787f4665ef3ae3859b462","cross_cats_sorted":["math.CO","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-12T20:00:05Z","title_canon_sha256":"e0d71630587a74e3b443560485ebeb8ab269b1d5899f96a5eaf7ea56e04c4d18"},"schema_version":"1.0","source":{"id":"1807.04804","kind":"arxiv","version":3}},"canonical_sha256":"66532a80f866876a2d3d556949b5073a6d584437afd438cc26ac3353e44a1120","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66532a80f866876a2d3d556949b5073a6d584437afd438cc26ac3353e44a1120","first_computed_at":"2026-07-05T00:50:00.192846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:50:00.192846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cyAljATAGQPHE8sdCl89PJ0dlhXaNxxwFfXk33T78Jl1ptf8Cc5x8rh5XahzQkTsswoEk5n1vUW4dvGDrs97CA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:50:00.193254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.04804","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0c5cf3af2d48df7a05b0f0037e267e6b695d159cbcdeb569efdf287ca087266","sha256:e53dfd3fa12e2287f4e489caaa8bdd662bb951e2c953f673f663442d5774cdc1"],"state_sha256":"74c9dedd4e65211d059ff13c570f8748fe42d56ca774b3ce918531d98ce315d8"}